Waclaw Sierpinski

Wacław Sierpiński was a Polish mathematician who lived from the late 19th to early 20th centuries C.E. In addition to his many contributions to set theory, number theory, and topology, he discovered three well known fractals the Sierpiński Gasket, Sierpiński Carpet, and Sierpiński Curve.

For the 2008 Joint Mathematics Meeting in San Diego, California, I created a picture of Sierpiński using iterations of the Sierpiński carpet. Eight different iterations were used, four each from a white and black square.

Using Java, I took the source image, averaged over 4x4 squares of pixels, and replaced each square of pixels with the iteration of the Sierpiński carpet which most closely approximated the grayscale value of the pixels it would replace. After placing a square, I diffused the error over the nearby squares using a Floyd-Steinberg based algorithm. I created a similar portrait using Sierpiński gaskets and the pair of portraits were displayed at the 2009 Bridges Math Art meeting.